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Superheavy quasi-atoms and quantum electrodynamics in strong fields
Nuclear Instruments and Methods North-Holland, Amsterdam
Section
in Physics
Research
747
B9 (1985) 747-752
VI. Novel aspects of highly ionised atoms
SUPERHEAVY QUASI-ATOMS IN STRONG FIELDS
AND QUANTUM
ELECTRODYNAMICS
G. SOFF GSI Darmstadt, POB I1 0 541, D - 6100 Darmstadt, Fed. Rep. Germany
U. MOLLER,
T. DE REUS, J. REINHARDT,
B. MOLLER
and W. GREINER
Instiiut fir Theoretische Physik, Uniuersitiit Frankfurt, Robert-Mayer -Sirasse 8 -10, D 6000 Frankfurt, Red. Rep. Germany
Distinct peak structures have been observed in spectra of positrons emitted in collisions of very heavy ions such as U-Th, U-U, Th-Cm and U-Cm. Characteristic features of these structures are discussed and confronted with our theoretical results. It is argued that this experimental finding could be associated with the spontaneous positron emission in the strong Coulomb field of giant nuclear
molecules
In collisions of very heavy ions with projectile energies close to the nuclear Coulomb barrier superheavy quasiatoms are formed for a short period of time Tlo-*’ s. In these exotic systems binding energies E, and wavefunctions of electrons are determined by the combined charge of the projectile and target nucleus. For the innermost electrons E, is comparable to the electron rest mass, the spatial distribution of electrons is localized within the Compton wavelength. Relativistic effects dominate completely the electron excitation processes. The related X-ray production and electron emission probability is treated extensively in refs. [l-8]. As the most fascinating feature the quasiatomic K-shell enters as a resonance state the negative energy continuum in overcritical systems (Z > 173). In principle this allows for spontaneous positron production provided a partial K-shell depletion has occurred on the ingoing path of the Rutherford trajectory. However, even for the heaviest colliding system investigated up to now, U + Cm with Z = 188, this overcritical scenery (E, > 2 m,c2) exists only for about 2 x lO-*i s whereas the spontaneous decay width corresponds to r - lOpI9 s. In consequence this peculiar particle creation process remains undetectable in elastic Rutherford scattering. To overcome this obstacle nuclear reactions were investigated theoretically [8-151 leading to a prolonged overcritical field configuration. As one particular aspect of spectroscopy studies in superheavy atomic systems we summarize in this paper the current information on measured line structures in positron spectra. The relationship of the experimental facts [16-201 and our hypothesis of spontaneous positron emission in the strong Coulomb field of giant nuclear molecules is illustrated. Fig. 1 shows positron spectra from U + U collisions 0168-583X/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
measured by Clemente et al. [17]. Different windows for the ion scattering angle 8,, and the bombarding energies 5.7, 5.9 and 6.2 MeV/u are considered. For central collisions the distance of closest approach corresponds approximately to the strong interaction radius. About 30% of the detected positrons result from nuclear excitations and subsequent internal pair creation. Superimposed on the smooth spectra, a line emerges at about 300 keV kinetic positron energy with centroid, width and intensity depending on both bombarding energy and ion scattering angle [17]. For the bombarding energy of 5.7 MeV/u the line appears at E,+= (308 + 15) keV for 38” < BLab < 52”, with a width of A E = (56 + 9) keV. The corresponding numbers for 5.9 MeV/u projectile energy are: E,+= (290 + 8) keV, A E = (81 k 9) keV for 40.5” < BLab < 49” and E,+= (281 k 7) keV, AE = (73 + 8) keV for 25.5’ < BLab < 38’. In contrast to the measurements of Clemente et al. [17] the positron spectrum detected by Backe et al. [16] at 5.9 MeV/u beam energy in coincidence with particles scattered to 45” + 10” does not indicate the presence of a line. For the highest bombarding energy (6.2 MeV/u) and 25.5” -= eLab < 32” (cf. fig. 1) again a sharp line appears [17] at E,+= (254 f 15) keV with A E = (81 f 18) keV. The e+-spectrum for the system U-Th (Z = 182) at E Lab= 5.9 MeV/u is displayed in fig. 2. It exhibits [17] a structure at E,+= (310 k 14) keV with a width of (110 + 25) keV. This structure shifts to lower positron energies E,+ = (290 + 7) keV, AE = (61 + 12) keV, if one detects the scattered particles in an angular window of 25.5” < eLab < 38”. This behaviour is similar to the line shift observed for the U + U system. However, the line intensity is smaller in the lower Z-system. The solid lines a in figs. 1 and 2 represent the VI. NOVEL
ASPECTS
748
G. Soff et al. / Superheavy
I
1
I
quasi-atoms
I
I
I
I
1
EIA=5.7MeVIu
b
E/A=5.9MeVlu
ElA=5.9MeVlu 1.6
0.8
0,
:
:
I
:
:
:
:
:
EIA=6.2MeVlu
5tt t a
3 L: 2
P
I
l0
0
t
Lo.5°4,,b
”
200
”
LOO
“I“
600
800
"$
l 0
I 200
l
'25.5°<~,.b;32; LOO
600
800
Ec.[c.m.llkeV Fig. 1. Positron creation probability per energy interval and scattered U nucleus versus the positron kinetic energy E,+ for U-U collisions at 5.7, 5.9 and 6.2 MeV/u bombarding energy and scattering angles as indicated [17].
theoretical result [7,8,21] for the dynamically positron formation. In fig. 1 the computed values are multiplied (171 by a scaling factor s, which serves to adjust the theoretical production probability of high energy positrons to the measured data. s is determined by a least-square fit procedure and varies between 0.8 and 1.2. The spectral shape of the high energy positrons is well reproduced by our calculations [7], which are based on a coupled channel analysis of the collision dynamics.
Electron screening corrections are taken into account by evaluating bound and continuum state wavefunctions for a relativistic Hartree-Fock-Slater potential [7]. For a detailed description of the theoretical formalism we refer to refs. [7,8,10,11,21]. The curves b in figs. 1 and 2 are a fit to the measured peak structures following a suggestion [lo] that the positron line originates from spontaneous positron decay of a K-hole in the overcritical field of giant nuclear molecules. The utilized form is
149
G. Soffet al./ Superheavy quasi-atoms IIll
1
Ill11
5,0
dP/dE(e’)
[10e7 keV-‘I
_
E/A = 5.9 MeVlu
u+u
L.5 -
5.7 MeV/u
L-0 -
38”
< 8 < 52O
-
3.53.02.52.0x
3
Qd
w
1.4 -
u+Th
s cl! 1.2 Q l.O-
E IA = 5.9 MeVlu 25.5’<&,<
1.5-
38” 1.0-
b-
ATDHF: s = 1.18 T = 7 c 10-20s q = 1.1 l 10-3
0.5
0.8 -
0.01 ’
’
’
’
200
100
0.6 -
1
’
300
’
’
400
500
E(e+)
3 ’
’
’
600
1
’
’
700
600
1
[keVl
0.4 5.0
O.:: 0
dP/dE(e’)
II
[10e7 keV’1
I - I - I r I - I.
1
200
LOO
600
800
E,+ 1c.m.l keV Fig. 2. The same as in
u+u
4.5-
1000
5.9 MeV/u
4.0-
fig. 1 for U-Th collisions at 5.9 MeV/u
bombarding energy.
I
40.5”
T
< 8 < 49O i
3.53.0-
PO1 dP,+/dE,+-
(T*/T)(sin(x)/x)*,
with x = (E,+-
E,)
(1)
T/2 h and the K-hole
diving energy Expression (1) is valid if the nuclear contact time T is small compared to the spontaneous decay time 7 (= 3 X lo-l9 s for U + U) (cf. also refs. [22,23]). This leads to a width [lo] of r = 5.56tt/T. E, and r are used as parameters to determine the curves b. Clemente et al. [17] furthermore carefully investigated nuclear excitations and pair conversion as a possible source of the positron peaks. By a detection of the electron spectra and the photon yield it could be concluded that conversion processes in the projectile or target nucleus are not responsible for the observed positron lines. For a closer theoretical inspection we again consider in fig. 3b the energy distribution of positrons measured [17] in U + U collisions at 5.9 MeV/u. The narrow line structure is well reproduced in our calculations [8] if we assume the formation of a giant nuclear quasimolecule for a period of time T> 5 X lo-*’ s. The distance E,
= -Et
2.5-
- 2m,c2.
ATDHF: s = 1.01 T = 5 c 10-20s q = 1.2
0.01 ’
100
’ 200
’
’ 300
’
’
400
l
’
E(e+)
10-3 ’
500
’
’ - ’ 600 700
’
’
600
1
LkeVl
Fig. 3. The same as in fig. 1 for 5.7 and 5.9 MeV/u projectile energy. The solid lines [8] follow from a theoretical analysis in an adiabatic approximation to the time-dependent Hartree-Fock formalism (ATDHF). between the nuclear charge centres is taken to be R 11.5 fm. The mixing ratio q of time delayed collisions relative to ordinary Rutherford scattering events for the VI. NOVEL ASPECTS
G. Sojj et al. / Superheavy quasi-atoms
750
measurement of the photon yield and a folding with theoretical conversion coefficients 1241. For the system U + Sm only conversion positrons could be detected. The solid lines which represent the final theoretical outcome plus the nuclear background contribution agree totally with the experimental data. This demonstrates the quality of the coupled channel calculations which reproduce adequately the positron production rate as a function of the positron energy, impact parameter, bombarding energy and combined nuclear charge. Experimental positron data [l&20] for the heaviest colliding system investigated until now, U + Cm, are displayed in fig. 5 for the bombarding energy of ELab = 6.05 MeV/u and 100” I&, < 130”. The spectra axe not corrected with respect to the detector efficiency. To allow for a comparison with theoretical results the calculated probabilities have been folded with the exefficiency. The nuclear background contriperimental bution has been added to the theoretical values. The lower part of the figure shows the positron emission
chosen angular window amounts to 4 - 1.2 x 10-3. In consequence we obtain for the related nuclear reaction cross section oN - 12 mb. In summary a total of four parameters (s, T, R, q) is employed. To reproduce the dominant line in the low energy domain at E,+= (308 + 15) keV measured [17] in U + U collisions at a bombarding energy of ELab = 5.7 MeV/u (fig. 3a) we deduce the following parameters: s - 1.18, T - 7 X 10d20 s, R - 11.5 fm, q - 1.1 x 10-3, which yields oN - 12 mb. Especially for this spectrum an accurate theoretical analysis suffers from strong fluctuations of the experimental data around the theoretical curve for E,+ B 350 keV. The EPOS collaboration [18-201 measured positron spectra for the systems 238U + 154Sm, 238U f 208Pb, 238U + 238U and 238U + 24*Cm and for ion scattering angles probability of 25” -=ze,., < 65”. The differential positron emission with respect to the positron kinetic energy is presented in fig. 4. The dashed lines indicate the nuclear background contribution determined via a 1-1
Total Positron Production:25" < QLAB < 65" I
‘II
I
’
I
’
238~
(a)
u
I
I
+ 154~~
’
I
’
(b)
200
400
600
+ 238U
800
I
’
1 (d)
,
238~
+ 2LBcrr
6.05 MeV/amu
1000
E,+
’
+ 208pb
5.9 MeV/amu
5.9 MeV/amu
0
I
238~
5.9 MeV/amu
238U
II
0
200
C keV
400
600
800
1000 1200
I
Fig. 4. Kinetic energy distribution of positron production probabilities averaged over the indicated ion lab angular region [ZO]. Dashed lines: nuclear
background;
solid lines: quasiatomic
theory [7,8,21] assuming
Rutherford
trajectories
together
with nuclear background.
G. Soff et al. / Superheavy quasi -atoms
1
U + Cm 30
EW = 6.05 MeVlu
20
In conclusion we presented a theoretical framework for the observed peaks in positron spectra. The study of the detailed dependence of the spontaneous positron emission on the beam energy and combined nuclear charge as well as the corresponding spectroscopy of the giant di-nuclear systems represent a very exciting task for the future. We are grateful for many fruitful cooperations with H. Backe, K. Bethge, H. Bokemeyer, T. Cowan I. Greenberg, P. Kienle, C. Kozhuharov, R. Krieg, D. Schwalm, P. Senger and K. Stiebing. G.S. acknowledges the support of the Deutsche Forschungsgemeinschaft (Heisenberg Programm).
10
0 20
References [l] Quantum Electrodynamics of Strong Fields, ed., W. Greiner, NASI Series B80 (Plenum, New York, 1983). [2] G.Soff, U. Muller, T. de Reus, P. Schliiter, A. Schafer, J.
10
0
-0
751
200
100
600
800
1000
1200
E(e+) IkeVl Fig. 5. Positron yield as observed for 238U + 248Cm collisions at a beam energy of 6.05 MeVJu 1181. No corrections with respect to Doppler broadening and the detector efficiency are performed: (a) 100” 5 BfM i 130°; (b) 50” < fJ,, < 80”. Dashed lines: theoretical folded yield for elastic Rutherford trajectories plus nuclear background; solid line: calculated result assuming in addition spontaneous positron formation in giant nuclear molecules [8].
rates for kinematical conditions (SO” < Sc, i 809, which suppress close collisions. The dashed line gives the theoretical yield for quasiatomic positron production [8] assuming elastic Rutherford trajectories together with the nuclear background. Fair agreement with the experimental values is achieved. For the angular window 100” I f?cM <: 130* a distinct peak emerges in the spectrum at E,+= (316 i 10) keV with a width of about A E - 80 keV [18]. Within the framework of our hypothesis of spontaneous positron production in giant nuclear molecules which are formed transiently at the closest encounter we analysed this narrow peak structure. Taking the parameters R - 16 fm, which corresponds approximately to the nuclear touching config uration, T >, lo-t9 s and 4 - I.3 X 10e3 (aN < 22 mb) we obtain agreement with the experimental facts. Furthermore the EPOS collaboration analysed carefully the y-ray as well as the a-electron yield to rule out the possible explanation of ordinary conversion processes as the origin of the narrow positron structures. No evidence for co~espond~ng nuclear transitions was found.
Reinhardt, B. Miiller and W. Greiner, in: NASI Series B 96, 177, ed.. R. Marrus (Plenum, New York, 1983). (31 H. Backe and C. Ko~uharov, in: Progress in Atomic Spectroscopy, Part C, eds., H.J. Beyer and H. Kleinpoppen, (Plenum, New York, 1984) p. 459. [4] C. Kozhuharov, in: Physics of Electronic and Atomic Collisions, ed., S. Datz (North-Holl~d, Amsterdam, 1982) p. 179. [5] PH. Mokier and D. Liesen, X-rays from superheavy cohision systems, in: Progress in Atomic Spectroscopy. Part C, eds. H.J. Beyer and H. Kleinpoppen (Plenum, New York, 1984) pi 321. [6] P.H. Mokler, Quasimolecular heavy ion-atom collisions,
Preprint GSI-84-37. [7] T.H.J. de Reus, J. Reinhardt, B. Miller, W. Greiner, G. Soff and U. Miller, J. Phys. 817 (1984) 615. [8] U. Muller, Atomare Anreg~gen in Schwe~onenst~ssen mit nuklearem Kontakt, Report GSI-84-7 (1984). [9] J. Rafelski, B. Mtller and W. Greiner, 2. Physik A285 (1978) 49. [lo] J. Reinhardt, U. Miiiier, B. Mtiler and W. Greiner, Z. Physik A303 (1981) 173. [ll] U. Miiler, G. Soff, T. de Reus, J. Reinhardt, B. Muller and W. Greiner, Z. Physik A313 (1983) 263. [12] W. Greiner, in: Proc. Int. Conf. Nucl. Phys., Vol. 2, Invited Papers, eds., P. Blasi and R.A. Ricci (Tipografia Compositori, Bologna, 1983) p. 635. [13] M.J. ~oades-Brown, V.E. Oberacker, M. Seiwert and W. Greiner, Z. Physik A310 (1983) 287. [14] U. Heinz, B. Miller and W. Greiner, Ann. Phys. 151 (1983) 227. [15] U. Heinz, J. Reinhardt, B. Muller, W. Greiner and U. Muller, Z. Physik A314 (1983) 125. [16] H. Backe, P. Senger, W. Bonin, E. Kankeleit, M. Kramer, R. Krieg, V. Metag, N. Trautmann and J.B. Wilhelmy, Phys. Rev. Lett. 50 (1983) 1838. [17] M. Clemente, E. Berdermann, P. Kienle, H. Tsertos, W. Wagner, C. Kozbuharov, F. Bosch and W. Koenig, Phys. Lett. 137B (1984) 41. VI. NOVEL
ASPECTS
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G. Soff et al. / Superheauy quasi-atoms
[IS] J. Schweppe et al., Phys. Rev. Lett. 51 (1983) 2261. 1191 D. Schwalm, in: Electronic and Atomic Collisions, eds., J. EichIer, I.V. Hertel and N. Stolterfoht (EIsevier Science Publishing, 1984) p. 295. [ZO] H. Bokemeyer. Positron spectroscopy of supercritical heavy ion collision systems, Proc. of the 19th Winter School on Physics, Zakopane, Poland, Preprint GSI-84-43 (1984)
(211 J. Reinhardt, B. Muher and W. Greiner, Phys. Rev. A24 (1981) 103. 1221 T. Tomoda and H.A. Weidenmtiher, Phys. Rev. C28 (1983) 739. 1231 J. Reinhardt, B. MiiIler, W. Greiner and U. Mtiller, Phys. Rev. A28 (1983) 2558. [24] P. Schlhter, G. Soff and W. Greiner, Phys. Rep. 75 (1981) 327.
Section
in Physics
Research
747
B9 (1985) 747-752
VI. Novel aspects of highly ionised atoms
SUPERHEAVY QUASI-ATOMS IN STRONG FIELDS
AND QUANTUM
ELECTRODYNAMICS
G. SOFF GSI Darmstadt, POB I1 0 541, D - 6100 Darmstadt, Fed. Rep. Germany
U. MOLLER,
T. DE REUS, J. REINHARDT,
B. MOLLER
and W. GREINER
Instiiut fir Theoretische Physik, Uniuersitiit Frankfurt, Robert-Mayer -Sirasse 8 -10, D 6000 Frankfurt, Red. Rep. Germany
Distinct peak structures have been observed in spectra of positrons emitted in collisions of very heavy ions such as U-Th, U-U, Th-Cm and U-Cm. Characteristic features of these structures are discussed and confronted with our theoretical results. It is argued that this experimental finding could be associated with the spontaneous positron emission in the strong Coulomb field of giant nuclear
molecules
In collisions of very heavy ions with projectile energies close to the nuclear Coulomb barrier superheavy quasiatoms are formed for a short period of time Tlo-*’ s. In these exotic systems binding energies E, and wavefunctions of electrons are determined by the combined charge of the projectile and target nucleus. For the innermost electrons E, is comparable to the electron rest mass, the spatial distribution of electrons is localized within the Compton wavelength. Relativistic effects dominate completely the electron excitation processes. The related X-ray production and electron emission probability is treated extensively in refs. [l-8]. As the most fascinating feature the quasiatomic K-shell enters as a resonance state the negative energy continuum in overcritical systems (Z > 173). In principle this allows for spontaneous positron production provided a partial K-shell depletion has occurred on the ingoing path of the Rutherford trajectory. However, even for the heaviest colliding system investigated up to now, U + Cm with Z = 188, this overcritical scenery (E, > 2 m,c2) exists only for about 2 x lO-*i s whereas the spontaneous decay width corresponds to r - lOpI9 s. In consequence this peculiar particle creation process remains undetectable in elastic Rutherford scattering. To overcome this obstacle nuclear reactions were investigated theoretically [8-151 leading to a prolonged overcritical field configuration. As one particular aspect of spectroscopy studies in superheavy atomic systems we summarize in this paper the current information on measured line structures in positron spectra. The relationship of the experimental facts [16-201 and our hypothesis of spontaneous positron emission in the strong Coulomb field of giant nuclear molecules is illustrated. Fig. 1 shows positron spectra from U + U collisions 0168-583X/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
measured by Clemente et al. [17]. Different windows for the ion scattering angle 8,, and the bombarding energies 5.7, 5.9 and 6.2 MeV/u are considered. For central collisions the distance of closest approach corresponds approximately to the strong interaction radius. About 30% of the detected positrons result from nuclear excitations and subsequent internal pair creation. Superimposed on the smooth spectra, a line emerges at about 300 keV kinetic positron energy with centroid, width and intensity depending on both bombarding energy and ion scattering angle [17]. For the bombarding energy of 5.7 MeV/u the line appears at E,+= (308 + 15) keV for 38” < BLab < 52”, with a width of A E = (56 + 9) keV. The corresponding numbers for 5.9 MeV/u projectile energy are: E,+= (290 + 8) keV, A E = (81 k 9) keV for 40.5” < BLab < 49” and E,+= (281 k 7) keV, AE = (73 + 8) keV for 25.5’ < BLab < 38’. In contrast to the measurements of Clemente et al. [17] the positron spectrum detected by Backe et al. [16] at 5.9 MeV/u beam energy in coincidence with particles scattered to 45” + 10” does not indicate the presence of a line. For the highest bombarding energy (6.2 MeV/u) and 25.5” -= eLab < 32” (cf. fig. 1) again a sharp line appears [17] at E,+= (254 f 15) keV with A E = (81 f 18) keV. The e+-spectrum for the system U-Th (Z = 182) at E Lab= 5.9 MeV/u is displayed in fig. 2. It exhibits [17] a structure at E,+= (310 k 14) keV with a width of (110 + 25) keV. This structure shifts to lower positron energies E,+ = (290 + 7) keV, AE = (61 + 12) keV, if one detects the scattered particles in an angular window of 25.5” < eLab < 38”. This behaviour is similar to the line shift observed for the U + U system. However, the line intensity is smaller in the lower Z-system. The solid lines a in figs. 1 and 2 represent the VI. NOVEL
ASPECTS
748
G. Soff et al. / Superheavy
I
1
I
quasi-atoms
I
I
I
I
1
EIA=5.7MeVIu
b
E/A=5.9MeVlu
ElA=5.9MeVlu 1.6
0.8
0,
:
:
I
:
:
:
:
:
EIA=6.2MeVlu
5tt t a
3 L: 2
P
I
l0
0
t
Lo.5°4,,b
”
200
”
LOO
“I“
600
800
"$
l 0
I 200
l
'25.5°<~,.b;32; LOO
600
800
Ec.[c.m.llkeV Fig. 1. Positron creation probability per energy interval and scattered U nucleus versus the positron kinetic energy E,+ for U-U collisions at 5.7, 5.9 and 6.2 MeV/u bombarding energy and scattering angles as indicated [17].
theoretical result [7,8,21] for the dynamically positron formation. In fig. 1 the computed values are multiplied (171 by a scaling factor s, which serves to adjust the theoretical production probability of high energy positrons to the measured data. s is determined by a least-square fit procedure and varies between 0.8 and 1.2. The spectral shape of the high energy positrons is well reproduced by our calculations [7], which are based on a coupled channel analysis of the collision dynamics.
Electron screening corrections are taken into account by evaluating bound and continuum state wavefunctions for a relativistic Hartree-Fock-Slater potential [7]. For a detailed description of the theoretical formalism we refer to refs. [7,8,10,11,21]. The curves b in figs. 1 and 2 are a fit to the measured peak structures following a suggestion [lo] that the positron line originates from spontaneous positron decay of a K-hole in the overcritical field of giant nuclear molecules. The utilized form is
149
G. Soffet al./ Superheavy quasi-atoms IIll
1
Ill11
5,0
dP/dE(e’)
[10e7 keV-‘I
_
E/A = 5.9 MeVlu
u+u
L.5 -
5.7 MeV/u
L-0 -
38”
< 8 < 52O
-
3.53.02.52.0x
3
Qd
w
1.4 -
u+Th
s cl! 1.2 Q l.O-
E IA = 5.9 MeVlu 25.5’<&,<
1.5-
38” 1.0-
b-
ATDHF: s = 1.18 T = 7 c 10-20s q = 1.1 l 10-3
0.5
0.8 -
0.01 ’
’
’
’
200
100
0.6 -
1
’
300
’
’
400
500
E(e+)
3 ’
’
’
600
1
’
’
700
600
1
[keVl
0.4 5.0
O.:: 0
dP/dE(e’)
II
[10e7 keV’1
I - I - I r I - I.
1
200
LOO
600
800
E,+ 1c.m.l keV Fig. 2. The same as in
u+u
4.5-
1000
5.9 MeV/u
4.0-
fig. 1 for U-Th collisions at 5.9 MeV/u
bombarding energy.
I
40.5”
T
< 8 < 49O i
3.53.0-
PO1 dP,+/dE,+-
(T*/T)(sin(x)/x)*,
with x = (E,+-
E,)
(1)
T/2 h and the K-hole
diving energy Expression (1) is valid if the nuclear contact time T is small compared to the spontaneous decay time 7 (= 3 X lo-l9 s for U + U) (cf. also refs. [22,23]). This leads to a width [lo] of r = 5.56tt/T. E, and r are used as parameters to determine the curves b. Clemente et al. [17] furthermore carefully investigated nuclear excitations and pair conversion as a possible source of the positron peaks. By a detection of the electron spectra and the photon yield it could be concluded that conversion processes in the projectile or target nucleus are not responsible for the observed positron lines. For a closer theoretical inspection we again consider in fig. 3b the energy distribution of positrons measured [17] in U + U collisions at 5.9 MeV/u. The narrow line structure is well reproduced in our calculations [8] if we assume the formation of a giant nuclear quasimolecule for a period of time T> 5 X lo-*’ s. The distance E,
= -Et
2.5-
- 2m,c2.
ATDHF: s = 1.01 T = 5 c 10-20s q = 1.2
0.01 ’
100
’ 200
’
’ 300
’
’
400
l
’
E(e+)
10-3 ’
500
’
’ - ’ 600 700
’
’
600
1
LkeVl
Fig. 3. The same as in fig. 1 for 5.7 and 5.9 MeV/u projectile energy. The solid lines [8] follow from a theoretical analysis in an adiabatic approximation to the time-dependent Hartree-Fock formalism (ATDHF). between the nuclear charge centres is taken to be R 11.5 fm. The mixing ratio q of time delayed collisions relative to ordinary Rutherford scattering events for the VI. NOVEL ASPECTS
G. Sojj et al. / Superheavy quasi-atoms
750
measurement of the photon yield and a folding with theoretical conversion coefficients 1241. For the system U + Sm only conversion positrons could be detected. The solid lines which represent the final theoretical outcome plus the nuclear background contribution agree totally with the experimental data. This demonstrates the quality of the coupled channel calculations which reproduce adequately the positron production rate as a function of the positron energy, impact parameter, bombarding energy and combined nuclear charge. Experimental positron data [l&20] for the heaviest colliding system investigated until now, U + Cm, are displayed in fig. 5 for the bombarding energy of ELab = 6.05 MeV/u and 100” I&, < 130”. The spectra axe not corrected with respect to the detector efficiency. To allow for a comparison with theoretical results the calculated probabilities have been folded with the exefficiency. The nuclear background contriperimental bution has been added to the theoretical values. The lower part of the figure shows the positron emission
chosen angular window amounts to 4 - 1.2 x 10-3. In consequence we obtain for the related nuclear reaction cross section oN - 12 mb. In summary a total of four parameters (s, T, R, q) is employed. To reproduce the dominant line in the low energy domain at E,+= (308 + 15) keV measured [17] in U + U collisions at a bombarding energy of ELab = 5.7 MeV/u (fig. 3a) we deduce the following parameters: s - 1.18, T - 7 X 10d20 s, R - 11.5 fm, q - 1.1 x 10-3, which yields oN - 12 mb. Especially for this spectrum an accurate theoretical analysis suffers from strong fluctuations of the experimental data around the theoretical curve for E,+ B 350 keV. The EPOS collaboration [18-201 measured positron spectra for the systems 238U + 154Sm, 238U f 208Pb, 238U + 238U and 238U + 24*Cm and for ion scattering angles probability of 25” -=ze,., < 65”. The differential positron emission with respect to the positron kinetic energy is presented in fig. 4. The dashed lines indicate the nuclear background contribution determined via a 1-1
Total Positron Production:25" < QLAB < 65" I
‘II
I
’
I
’
238~
(a)
u
I
I
+ 154~~
’
I
’
(b)
200
400
600
+ 238U
800
I
’
1 (d)
,
238~
+ 2LBcrr
6.05 MeV/amu
1000
E,+
’
+ 208pb
5.9 MeV/amu
5.9 MeV/amu
0
I
238~
5.9 MeV/amu
238U
II
0
200
C keV
400
600
800
1000 1200
I
Fig. 4. Kinetic energy distribution of positron production probabilities averaged over the indicated ion lab angular region [ZO]. Dashed lines: nuclear
background;
solid lines: quasiatomic
theory [7,8,21] assuming
Rutherford
trajectories
together
with nuclear background.
G. Soff et al. / Superheavy quasi -atoms
1
U + Cm 30
EW = 6.05 MeVlu
20
In conclusion we presented a theoretical framework for the observed peaks in positron spectra. The study of the detailed dependence of the spontaneous positron emission on the beam energy and combined nuclear charge as well as the corresponding spectroscopy of the giant di-nuclear systems represent a very exciting task for the future. We are grateful for many fruitful cooperations with H. Backe, K. Bethge, H. Bokemeyer, T. Cowan I. Greenberg, P. Kienle, C. Kozhuharov, R. Krieg, D. Schwalm, P. Senger and K. Stiebing. G.S. acknowledges the support of the Deutsche Forschungsgemeinschaft (Heisenberg Programm).
10
0 20
References [l] Quantum Electrodynamics of Strong Fields, ed., W. Greiner, NASI Series B80 (Plenum, New York, 1983). [2] G.Soff, U. Muller, T. de Reus, P. Schliiter, A. Schafer, J.
10
0
-0
751
200
100
600
800
1000
1200
E(e+) IkeVl Fig. 5. Positron yield as observed for 238U + 248Cm collisions at a beam energy of 6.05 MeVJu 1181. No corrections with respect to Doppler broadening and the detector efficiency are performed: (a) 100” 5 BfM i 130°; (b) 50” < fJ,, < 80”. Dashed lines: theoretical folded yield for elastic Rutherford trajectories plus nuclear background; solid line: calculated result assuming in addition spontaneous positron formation in giant nuclear molecules [8].
rates for kinematical conditions (SO” < Sc, i 809, which suppress close collisions. The dashed line gives the theoretical yield for quasiatomic positron production [8] assuming elastic Rutherford trajectories together with the nuclear background. Fair agreement with the experimental values is achieved. For the angular window 100” I f?cM <: 130* a distinct peak emerges in the spectrum at E,+= (316 i 10) keV with a width of about A E - 80 keV [18]. Within the framework of our hypothesis of spontaneous positron production in giant nuclear molecules which are formed transiently at the closest encounter we analysed this narrow peak structure. Taking the parameters R - 16 fm, which corresponds approximately to the nuclear touching config uration, T >, lo-t9 s and 4 - I.3 X 10e3 (aN < 22 mb) we obtain agreement with the experimental facts. Furthermore the EPOS collaboration analysed carefully the y-ray as well as the a-electron yield to rule out the possible explanation of ordinary conversion processes as the origin of the narrow positron structures. No evidence for co~espond~ng nuclear transitions was found.
Reinhardt, B. Miiller and W. Greiner, in: NASI Series B 96, 177, ed.. R. Marrus (Plenum, New York, 1983). (31 H. Backe and C. Ko~uharov, in: Progress in Atomic Spectroscopy, Part C, eds., H.J. Beyer and H. Kleinpoppen, (Plenum, New York, 1984) p. 459. [4] C. Kozhuharov, in: Physics of Electronic and Atomic Collisions, ed., S. Datz (North-Holl~d, Amsterdam, 1982) p. 179. [5] PH. Mokier and D. Liesen, X-rays from superheavy cohision systems, in: Progress in Atomic Spectroscopy. Part C, eds. H.J. Beyer and H. Kleinpoppen (Plenum, New York, 1984) pi 321. [6] P.H. Mokler, Quasimolecular heavy ion-atom collisions,
Preprint GSI-84-37. [7] T.H.J. de Reus, J. Reinhardt, B. Miller, W. Greiner, G. Soff and U. Miller, J. Phys. 817 (1984) 615. [8] U. Muller, Atomare Anreg~gen in Schwe~onenst~ssen mit nuklearem Kontakt, Report GSI-84-7 (1984). [9] J. Rafelski, B. Mtller and W. Greiner, 2. Physik A285 (1978) 49. [lo] J. Reinhardt, U. Miiiier, B. Mtiler and W. Greiner, Z. Physik A303 (1981) 173. [ll] U. Miiler, G. Soff, T. de Reus, J. Reinhardt, B. Muller and W. Greiner, Z. Physik A313 (1983) 263. [12] W. Greiner, in: Proc. Int. Conf. Nucl. Phys., Vol. 2, Invited Papers, eds., P. Blasi and R.A. Ricci (Tipografia Compositori, Bologna, 1983) p. 635. [13] M.J. ~oades-Brown, V.E. Oberacker, M. Seiwert and W. Greiner, Z. Physik A310 (1983) 287. [14] U. Heinz, B. Miller and W. Greiner, Ann. Phys. 151 (1983) 227. [15] U. Heinz, J. Reinhardt, B. Muller, W. Greiner and U. Muller, Z. Physik A314 (1983) 125. [16] H. Backe, P. Senger, W. Bonin, E. Kankeleit, M. Kramer, R. Krieg, V. Metag, N. Trautmann and J.B. Wilhelmy, Phys. Rev. Lett. 50 (1983) 1838. [17] M. Clemente, E. Berdermann, P. Kienle, H. Tsertos, W. Wagner, C. Kozbuharov, F. Bosch and W. Koenig, Phys. Lett. 137B (1984) 41. VI. NOVEL
ASPECTS
152
G. Soff et al. / Superheauy quasi-atoms
[IS] J. Schweppe et al., Phys. Rev. Lett. 51 (1983) 2261. 1191 D. Schwalm, in: Electronic and Atomic Collisions, eds., J. EichIer, I.V. Hertel and N. Stolterfoht (EIsevier Science Publishing, 1984) p. 295. [ZO] H. Bokemeyer. Positron spectroscopy of supercritical heavy ion collision systems, Proc. of the 19th Winter School on Physics, Zakopane, Poland, Preprint GSI-84-43 (1984)
(211 J. Reinhardt, B. Muher and W. Greiner, Phys. Rev. A24 (1981) 103. 1221 T. Tomoda and H.A. Weidenmtiher, Phys. Rev. C28 (1983) 739. 1231 J. Reinhardt, B. MiiIler, W. Greiner and U. Mtiller, Phys. Rev. A28 (1983) 2558. [24] P. Schlhter, G. Soff and W. Greiner, Phys. Rep. 75 (1981) 327.